7 Answers
7

See pg. 127 ff. of this publication from YCT. It is an article by Jason Weiner titled "ON THE HALAKHIC BASIS FOR WEARING BLACK HATS". In this article he discusses 5 reasons given by the Rabbinical Authorities for wearing a black hat:

Reason 2 makes me pause. During the criminal trial of a black-fedorah-wearing (but unbearded) Orthodox Jew, some in the national press thought it was amusing that the accused criminal should wear a hat that was popular with gangsters in the 1920s and 1930s. If we are trying to "distinguish ourselves from the other nations," the selection of the style of hat may have been a poor choice.
– Bruce JamesFeb 11 '13 at 17:26

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@BruceJames Right, and so too the "bent-up" hats are worn by the Amish. And Viznitz chassidim apparently wear their "beaver" hats backwards because their Rebbe once walked next to a priest who had an identical hat. The Rebbe turned his around to distinguish. I guess Satmar etc. have an argument for wearing their style of flat "beaver" hats, as I don't know of any gentiles wearing that style.
– AdámJan 6 '14 at 17:32

I am new to wearing hats on שבת and יום טוב. Do you wear a white hat on יום כיפור?
– Joshua PearlSep 11 '14 at 17:22

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@JoshuaPearl, in German-Jewish communities, those who wear a hat during the year typically will not wear one on R"H/Y"K. We will wear a white käppchen, which is a bit like the kippot you'd see in photos of R' Kotler or R' Elyashiv
– Noach MiFrankfurtMar 25 '15 at 17:37

The Chayei Adam says for birkas hamazon, "and wear a hat, like any respectable person would do if they were walking in the street."

R' Yitzchak Hutner once told a fellow: "wear a hat. A yarmulka is too easy to fold up and put in your pocket if you get embarrassed of being Jewish." (Very similar to the Lubavitcher Rebbe's letter about sheitels vs. kerchiefs.)

The curious thing is that all of the old European (specifically) Litvaks I know take off their yarmulkes and put them in their pockets when they put on their black hat. Then when they take off their hat, they discretely slide the yarmulke back on underneath as they remove the hat. But the younger, born in America generation that I am familiar with, wears both the hat and yarmulke together.
– CuriouserOct 18 '11 at 16:19

@Curiouser As far as I remember, that is actually the main halacha.
– AdámJan 6 '14 at 17:27

The Zohar is meramez that a talmid chacham needs an extra level of head covering, especially upon saying a davar shebik'dusha. Regarding the hat, it not only is a second cover, but it is bigger and more demonstrative of one's devotion.

The Zohar adds, for instance, that one should wrap oneself with a tallis during davening; apparently, standing with a kippah is not enough. The same wrapping concept would apply to a hat that hovers above the head very much like a tallis, albeit slightly less.

All of these head coverings indicate deference to someone greater, and that we commit to G-D's commands even when we cannot understand and even if our ideas conflict with it; we still accept.

Look in Aruch Hashluchan in Hilchos Dayanim and Birkas Hamazon where he mentions that Atifa (enwrapment) mentioned in SA is applied nowadays through a hat (and possible jacket, I don;t have an Aruch Hashulchan on me).

The main reason people wore hats during davening was because that's what they would wear when in front of someone important. Nowadays, they mainly wear it so as not to change from before, or to differentiate themselves from other people. The two-layer thing is not in the Shulchan Aruch, but if one does want to follow it, I could see why one item wouldn't make the cut.

You are correct as far as the facts stating people's reasons. However, I've always thought the diffrentiating part is ridiculous. Whenever it was people decided to wear the hats like everybody else nobody seemed to care about being different and not changing old ways of dressing. And not only did they not care but it even became halachicly binding in order to be dressed normally.
– user6591Jun 18 '14 at 11:15

Having two layers bidieved fulfills this. A separate hat is considered better than just the two layers of the kipa. The main reason for two layers in a kipa is in case one might not have their hat with them at all times and at some point will want to make a bracha on food.

The idea of getting dressed up in a more respectful manner to speak with Hashem.

Likewise if one would wear nice clothing to see someone important there is a kal vachomer to prayer.